# Find the Maximum/Minimum Value f(x)=-x^2-5x-2 The maximum or minimum of a quadratic function occurs at . If is negative, the maximum value of the function is . If is positive, the minimum value of the function is .
occurs at
Find the value of equal to .
Substitute in the values of and .
Remove parentheses.
Simplify .
Multiply by .
Dividing two negative values results in a positive value.
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Raise to the power of .
Multiply .
Multiply by .
Combine and .
Multiply by .
Find the common denominator.
Multiply by .
Combine.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Multiply by .
Combine fractions.
Combine fractions with similar denominators.
Multiply.
Multiply by .
Multiply by .
Simplify the numerator.
Subtract from .
The final answer is .
Use the and values to find where the maximum occurs.
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